CPM Homework Help : PC Problem 4-53

For each graph below, find an equation using sine and an equation using cosine that will generate the graph. For each graph, one of the functions you find should not require a horizontal shift.

Hint (a):

Added to periodic curve, 3 horizontal lines at, y = negative 5, y = negative 2, & y = 1.

Added: vertical up arrow at x = 3 halves pi, from middle horizontal to top horizontal.

Added: horizontal double sided arrow from (0, comma negative 2), to (2 pi, comma negative 2).

Added: vertical down arrow at x = 1 half pi, from top horizontal to middle horizontal.

Step 1(a):

Draw a horizontal line through the center, top, and bottom of the curve.

Step 2(a):

The amplitude is from the middle up to the top of the curve.

Step 3(a):

The period is the length of one cycle. In this case it is $2π$ , so $F = 1$ .

Step 4(a):

Shifts: Horizontal (left or right shift from $y$ -axis). Vertical (up or down shifts from $x$ -axis.)

Use the eTool below to visualize this problem.
Click on the link to the right to view the full version of the eTool: PCT 4-53 eTool